The simplified story is that the strong nuclear force makes nucleons bind to each other. The more nucleons there are around, the more partners any one nucleon has available to bind to. That's the reason for the rising binding energy to begin with. It stops growing as the neighborhood of each nucleon becomes full since nuclear binding is short range. The force opposing stability is electrostatic repulsion between the protons. Which just keeps growing as protons are added since it is a long range force. By the time you get up to uranium, the nucleus is just about ready to spontaneously fall apart.